Related papers: On the Representation and State Complexity of Bloc…
The determination of block-entropies is a well established method for the investigation of discrete data, also called symbols (7). There is a large variety of such symbolic sequences, ranging from texts written in natural languages,…
An index for a finite automaton is a powerful data structure that supports locating paths labeled with a query pattern, thus solving pattern matching on the underlying regular language. In this paper, we solve the long-standing problem of…
We characterize complete deterministic finite automata with two input letters in which every non-empty set of states occurs as the image of the whole state set under the action of a suitable input word. The characterization leads to a…
This paper is an extended abstract of the dissertation presented by the author for the doctoral degree in physics and mathematics (in Russia). The main characteristic studied in the dissertation is combinatorial complexity, which is a…
Finite-state complexity is a variant of algorithmic information theory obtained by replacing Turing machines with finite transducers. We consider the state-size of transducers needed for minimal descriptions of arbitrary strings and, as our…
A set of integers is $S$-recognizable in an abstract numeration system $S$ if the language made up of the representations of its elements is accepted by a finite automaton. For abstract numeration systems built over bounded languages with…
Although transformers are remarkably effective for many tasks, there are some surprisingly easy-looking regular languages that they struggle with. Hahn shows that for languages where acceptance depends on a single input symbol, a…
Maintaining efficient semantic representations of the environment is a major challenge both for humans and for machines. While human languages represent useful solutions to this problem, it is not yet clear what computational principle…
For a language $L$, we consider its cyclic closure, and more generally the language $C^k(L)$, which consists of all words obtained by partitioning words from $L$ into $k$ factors and permuting them. We prove that the classes of ET0L and…
The similarity of the evolution of human languages (or alphabets, bird songs, >...) to biological evolution of species is utilized to study with up to $10^9$ people the rise and fall of languages either by macroscopic differential equations…
The use of monoids in the study of word languages recognized by finite-state automata has been quite fruitful. In this work, we look at the same idea of "recognizability by finite monoids" for other monoids. In particular, we attempt to…
We study three levels in a hierarchy of nondeterminism: A nondeterministic automaton $\mathcal{A}$ is determinizable by pruning (DBP) if we can obtain a deterministic automaton equivalent to $\mathcal{A}$ by removing some of its…
Consider nondeterministic finite automata recognizing base-k positional notation of numbers. Assume that numbers are read starting from their least significant digits. It is proved that if two sets of numbers S and T are represented by…
We investigate the expressive power of first-order quantifications in the context of monadic second-order logic over pictures. We show that k+1 set quantifier alternations allow to define a picture language that cannot be defined using k…
We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…
Linguistic variables represent crisp information in a form and precision appropriate for the problem. For example, to answer the question "How are you?" one may say "I am fine." the linguistic variables like "fine", so common in everyday…
Partially ordered automata are automata where the transition relation induces a partial order on states. The expressive power of partially ordered automata is closely related to the expressivity of fragments of first-order logic on finite…
Compressing resource-intensive large language models by removing whole transformer blocks is a seemingly simple idea, but identifying which blocks to remove constitutes an exponentially difficult combinatorial problem. In this paper, we…
Communicating state machines provide a formal foundation for distributed computation. Unfortunately, they are Turing-complete and, thus, challenging to analyse. In this paper, we classify restrictions on channels which have been proposed to…
The end-to-end nature of neural machine translation (NMT) removes many ways of manually guiding the translation process that were available in older paradigms. Recent work, however, has introduced a new capability: lexically constrained or…